372 



PRACTICAL MATHEMATICS 



It should be noticed that the form of the final solution depends 

 upon the nature of the values of a; that is, according as R 2 is 



4L 



greater than, equal to, or less than -=-. The method of procedure 



K 



is exactly the same as that adopted for the analogous differential 



/I (tT 1 



equation -T-T- + 2a-r- + b z x = 0. 

 dt* dt 



EXAMPLES XXI 

 Solve the following differential equations : 



(2) 



ffiy 

 dx 2 



(11) __ = _ 20#, where x ft. is distance and t sees, is time, 



represents the equation of motion of a body. Find an expression 

 giving x in terms of t, when the initial conditions are (1) t = 0, 



fJ'YJ fj'TP 



x = 0-5, and -7- = ; (2) t = 0, x = 0, and -j- = 4 ; (3) t = 0, x = 0-5, 

 and | =4. 



